Weighted isoperimetric inequalities on ℝn and applications to rearrangements

Weighted isoperimetric inequalities on ℝn and applications to rearrangements

We study isoperimetric inequalities for a certain class of probability measures on ℝn together with applications to integral inequalities for weighted rearrangements. Furthermore, we compare the solution to a linear elliptic problem with the solution to some “rearranged” problem defined in the domai...

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Veröffentlicht in:Mathematische Nachrichten 2008-04, Vol.281 (4), p.466-498
Hauptverfasser: Betta, M. Francesca, Brock, Friedemann, Mercaldo, Anna, Posteraro, M. Rosaria
Format: Artikel
Sprache:eng
Schlagworte:
comparison results
Isoperimetric inequalities
Polya−Sz̈ego inequality
Steiner symmetrization
weights
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Zusammenfassung:We study isoperimetric inequalities for a certain class of probability measures on ℝn together with applications to integral inequalities for weighted rearrangements. Furthermore, we compare the solution to a linear elliptic problem with the solution to some “rearranged” problem defined in the domain {x: x1 < α (x2, …, xn)} with a suitable function α (x2, …, xn). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.200510619